Question

Mr and Mrs Smith buy tickets for themselves and their four children.
The cost of an adult ticket is £6 more than the adult ticket.
The total cost of the six tickets is £40.50
Work out the cost of an adult ticket.

In your working let c be the cost of the child ticket and a be the cost of the adult ticket.

Answer 1

The cost of an adult ticket is £6 more than that of a child ticket, so will be denoted by c+6. Now, we are told that the cost of four child tickets and two adult tickets is £40.50, so we can put this in an equation and solve for c:
(c+6)+(c+6)+c+c+c+c=40.50
6c+12=40.50
6c=28.50
c=4.75
Therefore the cost of a child's ticket (c) is £4.75 and the cost of an adult ticket (c+6) is £10.75.

Answer 2

The cost of the child ticket is £4.75 and the cost of the adult ticket is £10.75 and this can be determined by forming the linear equations in two variables.

Given :

• Mr. and Mrs. Smith buy tickets for themselves and their four children.
• The cost of an adult ticket is £6 more than the child ticket.
• The total cost of the six tickets is £40.50

The following steps can be  used in order to determine the cost of an adult ticket:

Step 1 - Let the cost of the child ticket be 'c' and the cost of the adult ticket be 'a'.

Step 2 - The linear equation that represents the situation that "the cost of an adult ticket is £6 more than the child ticket" is given by:

a = c + 6  --- (1)

Step 3 - The linear equation that represents the situation that "the total cost of the six tickets is £40.50" is given by:

2a + 4c = 40.50  --- (2)

Step 4 - Substitute the value of 'a' in the equation (2).

2(c + 6) + 4c = 40.50

2c + 12 + 4c = 40.50

6c = 28.5

c = £4.75

Step 5 - Substitute the value of 'c' in equation (1).

a = 4.75 + 6

a = £10.75

So, the cost of the child ticket is £4.75 and the cost of the adult ticket is £10.75.

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